Multicast rate optimization

ABSTRACT

This invention relates to multicast rate optimization, particularly a method for controlling an encoder ( 1 ) in a communications system ( 3 ) including a plurality of receivers ( 2 ). The method includes partitioning the receivers ( 2 ) into at least one cell, and associating each cell with a specific rate that may be used to transmit signals to a receiver ( 2 ). According to the inventive method, uncertainties in estimates of conditions of the communications system ( 3 ) are taken into account by modelling the conditions, such as the average distortion perceived by the receivers ( 2 ), as the outcome of a stochastic variable, thereby accounting for uncertainties in the estimates of the conditions of the communications system ( 3 ). The invention also relates to an encoder associated with the method.

This application is the National Phase of PCT/EP2009/060808 filed onAug. 20, 2009, which claims priority under 35 U.S.C. 119(e) to U.S.Provisional Application No. 61/090,811 filed on Aug. 21, 2008 and under35 U.S.C. 119(a) to Patent Application No. 08162702.8 filed in Europe onAug. 20, 2008, all of which are hereby expressly incorporated byreference into the present application.

FIELD OF THE INVENTION

The present invention relates to a method and a device for multicastrate optimization. In particular, the present invention relates to amethod for controlling an encoder in a communications system and anassociated device.

BACKGROUND OF THE INVENTION

Multicast is a bandwidth efficient technique for transmission of asource signal from a transmitter to a plurality of receivers in acommunications system. In general, an encoder is included in atransmitter, and a decoder is included in a receiver. As well known, thepurpose of encoding a signal is to achieve a compact representation ofthe signal. In general, such encoding is carried out according to one ormore of two basic coding principles, namely redundancy removal, that isexploiting signal properties that are predictable, e.g., the correlationbetween pixels in an image (spatial redundancy), the correlation betweenpixels in adjacent video signal frames (temporal redundancy), etc., andirrelevancy removal, that is exploiting the indifference of a receiverto certain variations in the signal representation, e.g., theindifference of a viewer to small quantization errors in a video signal.

The efficiency of multicast is mainly due to the fact that the encodingof the source signal needs to be transmitted only once over any link inthe communications system. However, the bandwidth efficiency comes withthe disadvantage that all receivers in the communications system areconstrained to use the same encoding of the source signal. Thus, everyreceiver perceives the same signal quality, which is determined by thebit-rate of the encoding, regardless of their respective capacity toreceive signals. In general, each receiver may have a different capacityto receive signals compared to the other receivers in the communicationssystem.

In general, coding systems need to take into account the reliability ofthe communications system in which they operate. In a communicationssystem, there is generally a certain probability of non-idealtransmission of signals, for example distorting the encoded signal ortransmitting only parts of the encoded signal. Furthermore, demands onthe coding systems may change rapidly due to variations in the load onthe communications system, inaccurate estimations of the capacity ofreceivers to receive signals, receivers joining and leaving thetransmission session, etc.

Advantageously, an encoder should therefore be able to quickly adapt tochanges in the estimated conditions of the communications system andaccount for uncertainty of the estimated conditions. Conventionalmethods for choosing the bit-rate of the encoding are based on iterativeprocedures having high computational complexity, see, e.g., Y. R. Yang,M. S. Kim, and S. S. Lam, “Optimal partitioning of multicast receivers”,Int. Conf. on Network Protocols, pp. 129-140, November 2000, H.Yousefi'zadeh, H. Jafarkhani, and A. Habibi, “Layered media multicastcontrol (LMMC): Rate allocation and partitioning”, IEEE/ACM transactionson Networking, vol. 13, pp. 540-553, 2005, and J. Liu, B. Li, and Y.-Q.Zhang, “Optimal stream replication for video multicasting”, IEEETransactions on Multimedia, vol. 8, pp. 162-169, 2006. Such conventionalmethods are particularly inefficient when the number of decodablesubsets of the streams is large.

Thus, there is a need within the art for a multicast bit-rateoptimization method such that the performance of the overall encodingand decoding system in a communications system is improved, which methodefficiently allows for a large number of decodable subsets of streams,as well as providing an improved adaptivity to varying conditions in thecommunications system and taking into account the uncertainty that isinherent in estimations of such conditions.

SUMMARY OF THE INVENTION

As already mentioned above, a key aspect of the multicast bit-rateoptimization problem is the time variance of the communications system,e.g., the load on the communications system, inaccurate estimations ofthe capacity of receivers to receive signals, receivers joining andleaving the transmission session, etc.

Thus, it is an object of the present invention to provide a method forcontrolling an encoder in a communications system including a pluralityof receivers such that the performance of the overall encoding anddecoding system in the communications system is improved.

It is a further object of the present invention to provide an apparatusfor performing such a method.

According to a first aspect of the present invention, there is provideda method for controlling an encoder in a communications system asdefined in the independent claim 1.

In the context of the present invention, the properties of the decodablesubsets of the streams preferably consists of, but are not limited to,transmission quality measures that have an impact on the overallencoder-decoder system performance.

By the method according to the first aspect of the invention,uncertainties in estimates of conditions of the communications systemare taken into account by modelling the conditions, in particular theaverage distortion perceived by the receivers, as the outcome of astochastic variable, where the stochastic nature of the model accountsfor uncertainties in the estimates of the conditions. Also, because theoutput of the method according to the first aspect of the inventiondepends on the estimates of the conditions, the method is adaptive tovarying conditions in the communications system.

According to a second aspect of the present invention, there is providedan encoder for use in a communications system including a plurality ofreceivers as defined in the independent claim 8.

The encoder according to the second aspect of the invention is adaptedto perform the method according to the first aspect of the invention,and thus the same advantages as for the first aspect of the inventionapply to the second aspect of the invention.

According to an embodiment of the present invention, it is preferred tochoose one or more cells of the subset of cells, and for each of the oneor more chosen cells determining if the condition (i) that thecontribution to the average distortion perceived by the receiverscontained in the cell and the bordering cells of said cell is minimalunder the conditions that the properties of the decodable subsets ofsaid cell and the bordering cells of said cell can be altered, and thatthe total size of said cell and the bordering cells of said cell cannotbe altered, is satisfied for the cell, and, if that is not the case,assigning a new value for the rate of the decodable subsets of thestreams that is associated with the cell, such that the condition (i)above is satisfied for the cell. This ensures that the averagedistortion perceived by the receivers, contained in the one or morecells and the bordering cells of said one or more cells, is minimal.

According to a further embodiment of the present invention, theproperties of the decodable subsets of the streams consists of one ormore of the following: the signal representation length per time unit,the error resilience, and the erasure resilience. These propertiesdirectly influence the perceived distortion by the receivers, and thusit is advantageous to be able to vary these properties during theprocess of controlling the encoder.

According to yet another embodiment of the present invention, feedbackinformation for the plurality of receivers is received, wherein thefeedback information includes a measure of a constraint on the rate thatmay be used to transmit signals to a receiver, wherein the constraintconsists of the available bandwidth for communicating with the receiver.

According to yet another embodiment of the present invention, theplurality of streams includes video or audio signals.

According to yet another embodiment of the present invention, theencoder includes a plurality of sub-encoders, each sub-encoderoutputting one stream, wherein each sub-encoder is provided with aproperty of the stream that is outputted by the sub-encoder. Thus,individual control of each sub-encoder is possible, thereby facilitatingoperation of the sub-encoder especially suited to the capacity of thesub-encoder.

According to yet another embodiment of the present invention, theencoder includes a layered (embedded) or multiple-description encoderoutputting a plurality of streams, which form a number of decodablesubsets, wherein the layered or multiple-description encoder is providedwith a property for each decodable subset that is outputted by saidlayered or multiple-description encoder. This provides, by analternative configuration, similar advantages to those for theembodiment of the invention described immediately above.

According to yet another embodiment of the present invention, eachstream of the plurality of streams is transmitted to one or morepredetermined receivers. In this manner, the communications system maybe regarded as a relay network for facilitating transfer of signalsbetween transmitters (encoders) and receivers. The total number ofstreams that a receiver may receive is equal to the number of decodablesubsets of the streams.

According to yet another embodiment of the present invention, it ispreferred to assign initial values for the rates of the decodablesubsets of the streams.

It is to be understood that it is within the scope of the invention thatthe features described above with reference to the different aspects andembodiments of the present invention, as well as the features disclosedin the appended claims, can be combined in an arbitrary manner. Forexample, according to one exemplary embodiment of the present invention,the method according to the first aspect of the invention furtherincludes receiving feedback information for the plurality of receivers,wherein the feedback information includes a measure of the rate that maybe used to transmit signals to a receiver, and furthermore, choosing oneor more cells of the at least one cell, and for each of the at least oneor more chosen cells determine if the condition (i) above is satisfiedfor the cell, and, if that is not the case, assign a new value for therate of the decodable subsets of the streams that is associated with thecell, such that the condition (i) above is satisfied for the cell.

BRIEF DESCRIPTION OF THE DRAWINGS

It should be understood that the exemplary embodiments of the presentinvention as shown in the figures are for purpose of exemplificationonly. Further embodiments and advantages of the present invention willbe made apparent when the figures are considered in conjunction with thefollowing detailed description and the appended claims.

Furthermore, it is to be understood that the reference signs provided inthe drawings are for the purpose of facilitating quicker understandingof the claims, and thus, they should not be construed as limiting thescope of the invention in any way.

FIG. 1 is a flowchart illustrating an embodiment of the presentinvention.

FIG. 2 is a schematic illustration of an embodiment of the presentinvention.

FIG. 3 is a schematic illustration of another embodiment of the presentinvention.

FIG. 4 is a schematic illustration of yet another embodiment of thepresent invention.

FIG. 5 is a flowchart for explaining the inventive theory underlying thepresent invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Preferred embodiments of the present invention will now be described forthe purpose of exemplification with reference to the accompanyingdrawings, wherein like numerals indicate the same elements throughoutthe views. It should be understood that the present inventionencompasses other exemplary embodiments that comprise combinations offeatures described in the following. Additionally, other exemplaryembodiments of the present invention are defined in the appended claims.

FIG. 1 is a schematic illustration of an exemplary embodiment of thepresent invention. In FIG. 1, a transmitter is denoted by the numeral 1.However, in the exemplary embodiment shown in FIG. 1, the transmitterincludes an encoder. Thus, in the following, for the purpose ofexplaining the invention, the term transmitter and the term encoder areinterchangeably used. However, this should not be construed as limitingthe present invention in any way.

The encoder 1 receives as input one or more signals (not shown) to betransmitted to receivers 2 via a communications system 3. According toexemplary embodiments of the present invention, said input signals areproduced by a video camera or the like or a microphone or the like, orby a combination of such devices. According to further exemplaryembodiments of the present invention, the communications system may be awireless network, such as the GSM network, a packet network, such as theInternet, or transmission mediums such as storage devices, e.g., compactdiscs, hard-disc drives, etc., or any other communications systemapparent for a person skilled in the art. In the exemplary embodiment ofthe present invention illustrated in FIG. 1, the number of receivers 2is four. However, it is the purpose that the invention encompasses otherexemplary embodiments of the present invention including any number ofreceivers.

As well known in the art, in the encoder 1, the input signal to betransmitted to the receiver 2 is encoded in order to achieve a morecompact representation of the signal, thereby facilitating communicationbetween the transmitter (encoder) 1 and a receiver 2. Furthermore, asalso well known in the art, a receiver in an encoding-decoding systemgenerally includes a decoder. Naturally, the purpose of the decoder isto decode an encoded signal transmitted from a transmitter (encoder).

The output of the encoder 1 consists of a plurality of streams 4, thestreams being of the kind that at least some subsets of the streams canbe decoded without knowledge of every stream of the plurality of streams4. Herein, such subsets of the streams are referred to as decodablesubsets. In the exemplary embodiment of the present inventionillustrated in FIG. 1, the number of streams 4 is three. However, it isthe purpose that the invention encompasses other exemplary embodimentsof the present invention including any number of streams. According toexemplary embodiments of the invention, the streams 4 include video oraudio signals.

Each of the receivers 2 receives at least one decodable subset of thestreams and preferably transmits feedback information to the encoder 1.This is represented by the multiple arrow points on the item designated5 in FIG. 1.

Thus, according to an exemplary embodiment of the present invention, theencoder 1 receives as input, apart from the one or more signalsmentioned above, feedback information 6 for the receivers 2 via thecommunications system 3. Preferably, the feedback information 6 is suchthat it includes a measure of the constraint on the rate that may beused to transmit signals to a receiver 2. According to anotherembodiment of the present invention, the constraint on the rate that maybe used to transmit signals to a receiver consists of the availablebandwidth for communicating with the receiver. Preferably, the encoder 1includes a control unit 7 that is adapted to receive said feedbackinformation 6.

FIG. 2 is a flowchart illustrating an exemplary embodiment of thepresent invention. In step 201, the plurality of receivers 2 containedin the communications system 3 are partitioned into at least one cell,where each cell is associated with a decodable subset of the streams.Furthermore, each of the decodable subsets is associated with a specificrate that may be used to transmit signals to a receiver. In exemplaryembodiments of the present invention, there is assigned initial valuesfor the rates of the decodable subsets of the streams. The assignment ofinitial values can be performed prior to step 201, or after step 201 butbefore step 202.

Next, for a subset of the at least one cell, there is determined in step202 if (i) the contribution to the average distortion perceived by thereceivers contained in the subset of cells and the bordering cells ofsaid subset of cells is minimal under the conditions that the propertiesof the decodable subsets of said subset of cells and the bordering cellsof said subset of cells can be altered, and that the total size of saidsubset of cells and the bordering cells of said subset of cells cannotbe altered. If such is the case, the encoder is controlled in step 205by outputting the decodable subsets of the streams in accordance withthe rates of the decodable subsets of the streams that are obtained whensteps 201 and 202 are performed.

In other words, if the rates that in step 201 were associated with thedecodable subsets of the streams satisfies the condition (i), the sodetermined rates are used for controlling the encoder by outputting thedecodable subsets of the streams in accordance with the so determinedrates.

However, if such is not the case, one or more cells of the subset ofcells is chosen in step 203, and for each of the one or more chosencells, there is determined in step 204 if the condition (i) is satisfiedfor the cell. If the condition (i) is satisfied for said one or morechosen cells, step 202 is performed again. If not, there is assigned anew value for the rate of the decodable subset of the streams that isassociated with a respective cell such that the condition (i) issatisfied for the cell, before step 202 is performed again.

According to exemplary embodiments of the present invention, the one ormore cells chosen in step 203 are chosen randomly, according to apredefined order, or are chosen so that for each of the one or morecells chosen, the average distortion perceived by the receiverscontained in the cells bordering the cell is decreased the most comparedto choosing any other cell.

The perceived distortion of the signals received by the receivers 2 isdirectly dependent on the rates of the decodable subsets of the streams,with the rates obtained as illustrated in FIG. 2. On the basis of therates of the decodable subsets of the streams, control signals 8 aresent from the control unit 7 to the encoder 1 for controlling theencoder 1. Therefore, the output from the control unit 7 has asignificant impact on the overall performance of the totalencoding-decoding system.

According to an exemplary embodiment of the present invention, theproperties of the decodable subsets of the streams consist of one ormore of the signal representation length per time unit, that is, therate, the error resilience, and the erasure resilience.

As illustrated in FIGS. 3 and 4, the control unit 7 provides controlsignals 8 to the encoder 1, the control signals 8 generally being suchthat based on the control signals 8, the encoder 1 can set appropriatevalues of the rates of the decodable subsets of the streams based oncurrent conditions in the communications system 3, as described abovewith reference to FIG. 2.

According to an exemplary embodiment of the present invention, theencoder 1 includes a plurality of sub-encoders 9, as illustrated in FIG.3, where each sub-encoder 9 outputs a single stream 4. According to saidembodiment of the present invention, the control unit 7 is adapted suchthat each sub-encoder 9 is provided with an estimate of a rate of thestream 4 that is outputted by said sub-encoder 9. Thus, according tosaid embodiment of the present invention, the control unit 7 canindividually control each sub-encoder 9, thereby facilitating operationof the sub-encoder 9 especially suited to the capacity of thesub-encoder 9.

An alternative embodiment of the present invention is illustrated inFIG. 4, wherein the encoder 1 includes a layered or multiple-descriptionencoder 10 outputting a number of streams 4 forming a number ofdecodable subsets, wherein the layered or multiple-description encoderis provided with a property for each decodable subset that is outputtedby said layered or multiple-description encoder. This provides, amongother things, the same advantage, by an alternative configuration of theencoder 1, as for the exemplary embodiment described immediately abovein conjunction with FIG. 3.

According to other embodiments of the present invention, each stream 4of the plurality of streams 4 outputted from the encoder 1 istransmitted to one or more predetermined receivers 2. In this way, thecommunications system 3 may be regarded as a relay network forfacilitating transfer of signals between transmitters (encoders) 1 andreceivers 2. The total number of streams 4 that a receiver 2 may receiveis equal to the number of decodable subsets of the streams 4.

According to an alternative, advantageous, exemplary embodiment of theinvention, there is provided a method for controlling an encoder in acommunications system including a plurality of receivers, wherein theencoder output consists of a plurality of streams of the kind that atleast some subsets of the streams can be decoded without knowledge ofevery stream of the plurality of streams, said method including thesteps of receiving feedback information from the communication systemfor each of the plurality of receivers, the feedback informationincluding a measure of a constraint on the rate, preferably consistingof the available bandwidth for communicating with the receiver, that maybe used to transmit signals to the receiver, modelling the measure by acontinuous stochastic variable while minimizing the distortion perceivedby the receiver, from which modelling estimates of transmission qualitymeasures of the decodable subsets of the streams are obtained andcontrolling the encoder to output the decodable subsets of the streamsin accordance with the thus obtained transmission quality measures ofthe decodable subsets of the streams. Preferably, a control unitincluded in an encoder is adapted to perform the steps of said method.In the following, the inventive theory underlying the present inventionis described.

Let the receivers in the communications system be numbered by the indexjε{1, . . . , J}, where the total number of receivers are J. A property(condition) of a communications system for a receiver j is given by aconstraint c_(j) on the rate that may be used to transmit signals to thereceiver. The constraint c_(j) may be construed as the availablebandwidth for communication with receiver j. It is assumed that theconditions of all receivers are realizations of a stochastic variablehaving a probability density function ƒ(c). This probability densityfunction characterizes the statistics of the conditions of thereceivers.

Let the distortion perceived by a receiver, receiving a decodable subsetat the rate r, be d(r). In principle, an arbitrary number of functionsmay be used to characterize the distortion d(r), two examples of whichare:

$\begin{matrix}{{{d(r)} = {a\; 2^{- {br}}}},{and}} & (1) \\{{d(r)} = {\frac{\theta}{r - R_{0}} + {D_{0}.}}} & (2)\end{matrix}$The parameters a, b, θ, R₀ and D₀ in equations (1) and (2) are modelparameters chosen such that d(r) corresponds to the distortion perceivedby the receiver. These parameters can, for example, be chosen in anoff-line search for the parameters that, via the model d(r), bestrepresent the perceived distortion. Further, these parameters may changeover time in order to better suit the signals, e.g., video signals, thatare being transmitted at any given instance.

The receivers may be partitioned into I disjoint sets, or cells, V_(i),where iε{1, . . . , I}. Each cell V_(i) is associated with areconstruction point r_(i) that is an approximation of the conditions(e.g., the rate constraint) of all the receivers belonging to the cellV_(i) for which one decodable subset of the streams is optimized. Letr={r_(i)}_(i=1) ^(I) denote the set of all I reconstruction points,where each reconstruction point r_(i) corresponds to one decodablesubset.

The partitioning of the receivers into cells V_(i) is determined by thecommunications system (possibly controlled by receiver preferences),which by relaying specific subsets of the streams to each receiver actsas a quantizer, characterized by an assignment function a(r,c_(j)). Theoutput of the assignment function is the reconstruction point r_(i), towhich a receiver is associated. The cell V_(i) is defined asV _(i) ={c:a(r,c)=r _(i)},  (3)where the assignment function is defined byr _(i) =a(r,c)={r _(i) :r _(i) ≦c≦r _(i+1) ,r _(i) εr}.  (4)The assignment function ensures that each receiver obtains the streamhaving the highest rate available, while not exceeding the constraint ofthe receiver.

The average distortion D perceived by the receivers is

$\begin{matrix}\begin{matrix}{D = {\sum\limits_{i = 1}^{I}{\int_{r_{i}}^{r_{i + 1}}{{d\left( {a\left( {r_{i},c} \right)} \right)}{f(c)}\ {\mathbb{d}c}}}}} \\{= {\sum\limits_{i = 1}^{I}{\int_{r_{i}}^{r_{i + 1}}{{d\left( r_{i} \right)}{f(c)}\ {\mathbb{d}c}}}}}\end{matrix} & (5)\end{matrix}$where r₀=0 and r_(I+1)→∞.

Now, let the cell width be defined by Δ_(i)=r_(i+1)−r_(i). For smallcell widths, or equivalently, a large number of cells, it is reasonableto assume that the probability density function ƒ(c) is constant withina cell, and that the distortion function d(c) varies linearly within acell. In quantization theory, this assumption is commonly referred to asthe high-rate assumption. Under these assumptions, the distortion withinthe cell V_(i) is

$\begin{matrix}{{\int_{r_{i}}^{r_{i + 1}}{{d\left( r_{i} \right)}{f(c)}\ {\mathbb{d}c}}} = {\int_{r_{i}}^{r_{i + 1}}{{d\left( {c - {\frac{1}{2}\Delta_{i}}} \right)}{f(c)}\ {{\mathbb{d}c}.}}}} & (6)\end{matrix}$

The variations of the cell width with respect to c can be approximatedby a function Δ(c) such thatΔ(r _(i))=Δ_(i).  (7)The inverse of Δ(c) represents the density of reconstruction points:g(c)=1/Δ(c).  (8)By integrating the density of reconstruction points, the total number ofreconstruction points is obtained:

$\begin{matrix}{{\int_{0}^{\infty}{{g(c)}\ {\mathbb{d}c}}} = {I.}} & (9)\end{matrix}$

Now, from equations (6), (7), and (8), the average distortion accordingto equation (5) is:

$\begin{matrix}{D = {\sum\limits_{i = 1}^{I}{\int_{r_{i}}^{r_{i + 1}}{{d\left( {c - {\frac{1}{2}{g^{- 1}(c)}}} \right)}{f(c)}\ {{\mathbb{d}c}.}}}}} & (10)\end{matrix}$In order to find the minimum distortion D, the density of reconstructionpoints g(c) is optimized by some optimization method, for example byapplying the method of Lagrange multipliers. The Lagrangian to beminimized is

$\begin{matrix}{{\Lambda = {\int_{0}^{\infty}{\left( {{{d\left( {c - {\frac{1}{2}{g^{- 1}(c)}}} \right)}{f(c)}} + {\lambda\;{g(c)}}} \right)\ {\mathbb{d}c}}}},} & (11)\end{matrix}$

where λ is a Lagrange multiplier. The optimum density of reconstructionpoints can be found by differentiating the above Lagrangian with respectto g(c), setting the thus obtained derivative equal to zero, and solvingfor g(c). Of course, other optimization techniques may be used.

According to one example, the distortion function d(r) is given byequation (1). By replacing d(r) in equation (11) with equation (1), theoptimal density of reconstruction points can be shown to be

$\begin{matrix}{{{g(c)} = {\frac{b}{4}{\ln(2)}\frac{1}{W\left( \sqrt{\frac{{- \lambda}\; 2^{c}{\ln(2)}}{8\;{{af}(c)}}} \right)}}},} & (12)\end{matrix}$where W(·) is the Lambert W function, defined according to:X=W(X)exp(W(X)).  (13)

According to another example, the distortion function d(r) is given byequation (2). By replacing d(r) in equation (11) with equation (2), theoptimal density of reconstruction points can be shown to be:

$\begin{matrix}{{g(c)} = {\frac{\frac{1}{2} + \sqrt{\theta\;{{f(c)}/2}\;\lambda}}{c - R_{0}}.}} & (14)\end{matrix}$

In order to obtain the set of reconstruction points r from the densityof reconstruction points g(c), a companding approach can be used. First,a compressor h(c) is defined as a monotonically increasing functionγ=h(c)  (15)that maps c to γ in the interval [0,1]. The compressor h(c) is such thatthe optimal quantization cells in the γ domain all have equal width. Byusing the relation between a random variable and its transform by amonotonic function, the density of reconstruction point density can beexpressed as

$\begin{matrix}\begin{matrix}{{g(c)} = {{g_{\Gamma}\left( {h(c)} \right)}{\frac{\partial{h(c)}}{\partial c}}}} \\{{= {I{\frac{\partial{h(c)}}{\partial c}}}},}\end{matrix} & (16)\end{matrix}$where it has been used that g_(Γ)(γ)=I. Then, reevaluating theLagrangian [equation (11)] for

${g(c)} = {I{\frac{\partial{h(c)}}{\partial c}}}$and solving for

${\frac{\partial{h(c)}}{\partial c}},$the following relation between the density of reconstruction points g(c)and the compressor h(c) can be found:

$\begin{matrix}{{h(c)} = {\frac{1}{I}{\int_{- \infty}^{c}{{g(c)}\ {{\mathbb{d}c}.}}}}} & (17)\end{matrix}$The optimal quantization cells are found by expanding the optimalquantization cells in the companded domain with the inverse of equation(17). The optimal reconstruction points are the reconstruction pointsfor which the distortion within the cells is minimized and thequantization cell widths are not altered. For cells {V_(i):i=2, . . . ,I}, the reconstruction points are set as the lower boundary, becausechoosing any other point would result in non-optimal quantization cellboundaries according to the assignment function in equation (4). This isnot the case for the first cell. Namely, choosing any reconstructionpoint within the cell effectively divides the cell into two subcells.The first subcell has the reconstruction point at rate zero, r₀=0, andall receivers assigned to r₀ are excluded from the multicast. The secondsubcell has the reconstruction point r₁ as its lower boundary. r₁ is setto the value that minimizes the expected distortion within the firstcell, that is

$\begin{matrix}{r_{1} = {{\underset{r_{1}}{\arg\;\min}{\int_{0}^{r_{1}}{{d(0)}{f(c)}\ {\mathbb{d}c}}}} + {\int_{r_{1}}^{r_{2}}{{d\left( r_{1} \right)}{f(c)}\ {{\mathbb{d}c}.}}}}} & (18)\end{matrix}$

The rate of the decodable subsets of the streams, that is the controlleroutput, is given by the so obtained reconstruction points that minimizesthe expected distortion.

Next, an alternative approach to determining the reconstruction pointsr_(i) using an iterative process is described.

The average distortion D can be divided into contributions d_(i) to thedistortion from each cell:

$\begin{matrix}{D = {{\sum\limits_{i = 1}^{I}{\int_{V_{i}}^{\;}{{d\left( {r_{i},\theta} \right)}{f(\theta)}\ {\mathbb{d}\theta}}}} = {\sum\limits_{i = 1}^{I}{d_{i}.}}}} & (19)\end{matrix}$A change in any element r_(i′) of the set of reconstruction points raffects the distortion of receivers in the cells that borders the cellV_(i′). Let the set S contain the cells that borders the cell V_(i′).Then, if r_(i′) is such that the distortion contributions of the cellsin S is minimal, according to

$\begin{matrix}{{r_{i^{\prime}} = {\underset{r_{1^{\prime}}}{\arg\;\min}{\sum\limits_{i \in S}{\int_{V_{i}}^{\;}{{d\left( r_{i} \right)}{f(c)}\ {\mathbb{d}c}}}}}},} & (20)\end{matrix}$r_(i′) is so called locally optimal.

The iterative process is illustrated in FIG. 5, wherein the processstarts in step 501.

In step 502, the elements of the set of reconstruction points r areassigned their initial values. The initial input, for instance values ofthe elements of r, can be chosen randomly or according to a predefinedinput.

In step 503, there is performed a convergence check by checking whethereach element of r is locally optimal according to equation (20). Ifconvergence is deemed to have been reached, the process ends (step 506).If convergence is deemed not to have been reached, step 504 isperformed.

In step 504, at least one element of r is chosen to be changed.According to one example, the element of r that is to be changed ischosen to be the element that gives the largest decrease in the averagedistortion D, when the element is changed according to equation (20).According to another example, the element of r that is to be changed ischosen according to some predefined order. According to yet anotherexample, the element of r that is to be changed is chosen randomly.

In step 505, the element of r chosen in step 504 is assigned a new valueaccording to equation (20). Thus, the new value of the specific elementof r is locally optimal.

After convergence has been reached, the iterative process ends in step506, whereafter the rate of the decodable subsets of the streams, thatis the controller output, is given by the so obtained reconstructionpoints.

Even though the present invention has been described with reference tospecific exemplifying embodiments thereof, many different alterations,modifications and the like will become apparent for those skilled in theart. The described embodiments are therefore not intended to limit thescope of the present invention, as defined by the appended claims.

Furthermore, any reference signs in the claims should not be construedas limiting the scope of the present invention. Also, in the claims, theindefinite article “a” or “an” does not exclude plurality.

The invention claimed is:
 1. A method for controlling an encoder in acommunications system including a plurality of receivers, wherein theencoder output consists of a plurality of streams, and wherein a firstdecodable subset of the plurality of streams is decoded independently ofa second decodable subset of the plurality of the streams, the methodincluding the steps of: (a) partitioning the plurality of receivers intoa plurality of cells, wherein each of the cells is associated with adecodable subset of the streams; (b) assigning an initial transmissionrate to each decodable subset of the streams based on an estimate ofavailable bandwidth for communicating with receivers in the cellassociated with the decodable subset of the streams; (c) for a firstcell of the plurality of cells, determining an average distortionperceived by the receivers in the first cell and the receivers in cellsbordering the first cell given the initial transmission rate assigned tothe decodable subset of the streams associated with the first cell; (d)determining whether the average distortion exceeds a thresholddistortion; (e) in response to determining that the average distortionexceeds the threshold distortion, assigning a new transmission rate tothe decodable subset of the streams associated with the first cell,wherein the new transmission rate is based on minimizing the averagedistortion perceived by the receivers in the cells bordering the firstcell; and (f) controlling the encoder to output the decodable subset ofthe streams associated with the first cell in accordance with the newtransmission rate assigned to the decodable subset of the streams;wherein the decodable subsets of the streams have one or more of thefollowing adaptable properties: the signal representation length pertime unit; the error resilience; and the erasure resilience.
 2. Themethod according to claim 1, wherein steps (c)-(e) are performed for oneor more other cells of the plurality of cells, and step (f) furthercomprises controlling the encoder to output the decodable subsets of thestreams associated with the one or more other cells in accordance withthe new transmission rates assigned to the decodable subsets of thestreams.
 3. The method according to claim 2, wherein the one or moreother cells are selected randomly, according to a predefined order, orsuch that for each of the one or more other cells selected, the averagedistortion perceived by the receivers contained in cells bordering thecell is decreased the most compared to choosing any other cell of theplurality of cells.
 4. The method according to claim 1, wherein theencoder includes one or more of the following: a plurality ofsub-encoders, each sub-encoder outputting one stream, wherein eachsub-encoder is provided with a property of the stream that is outputtedby the sub-encoder, and a layered or multiple-description encoderoutputting a plurality of streams forming a number of decodable subsets,wherein said encoder is provided with a property for each decodablesubset that is outputted by said encoder.
 5. The method according toclaim 1, further comprising receiving feedback information for theplurality of receivers, wherein the feedback information includes ameasure of the rate that may be used to transmit signals to a receiver.6. The method according to claim 1, wherein the plurality of streamsincludes video or audio signals.
 7. An encoder for use in acommunications system including a plurality of receivers, wherein theencoder output consists of a plurality of streams, and wherein a firstdecodable subset of the plurality of streams is decoded independently ofa second decodable subset of the plurality of the streams, the encoderincluding: a control unit configured to: (a) partition the plurality ofreceivers into a plurality of cells, wherein each of the cells isassociated with a decodable subset of the streams, (b) assign an initialtransmission rate to each decodable subset of the streams based on anestimate of available bandwidth for communicating with receivers in thecell associated with the decodable subset of the streams; (c) for afirst cell of the plurality of cells, determine an average distortionperceived by the receivers in the first cell and the receivers in cellsbordering the first cell given the initial transmission rate assigned tothe decodable subset of the streams associated with the first cell; (d)determine whether the average distortion exceeds a threshold distortion;(e) in response to determining that the average distortion exceeds thethreshold distortion, assign a new transmission rate to the decodablesubset of the streams associated with the first cell, wherein the newtransmission rate is based on minimizing the average distortionperceived by the receivers in the cells bordering the first cell; and(f) control the encoder by outputting the decodable subset of thestreams associated with the first cell in accordance with the newtransmission rate assigned to the decodable subset of the streams; andwherein the decodable subsets of the streams have one or more of thefollowing adaptable properties: the signal representation length pertime unit; the error resilience; and the erasure resilience.
 8. Theencoder according to claim 7, wherein the control unit is furtherconfigured to perform (c)-(e) for one or more other cells of theplurality of cells, and control the encoder by outputting the decodablesubsets of the streams associated with the one or more other cells inaccordance with the new transmission rates assigned to the decodablesubsets of the streams.
 9. The encoder according to claim 8, wherein thecontrol unit is further configured to select the one or more other cellsrandomly, according to a predefined order, or such that for each of theone or more other cells selected, the average distortion perceived bythe receivers contained in cells bordering the cell is decreased themost compared to choosing any other cell of the plurality of cells. 10.The encoder according to claim 7, further including one or more of thefollowing: a plurality of sub-encoders, each sub-encoder outputting onestream, wherein each sub-encoder is provided with a property of thestream that is outputted by the sub-encoder, and a layered ormultiple-description encoder outputting a plurality of streams forming anumber of decodable subsets, wherein said encoder is provided with aproperty for each decodable subset that is outputted by said encoder.11. The encoder according to claim 7, wherein the control unit isfurther adapted to receive feedback information for the plurality ofreceivers, wherein the feedback information includes a measure of therate that may be used to transmit signals to a receiver.
 12. The encoderaccording to claim 7, wherein the plurality of streams includes video oraudio signals.
 13. The method according to claim 2, wherein the encoderincludes one or more of the following: a plurality of sub-encoders, eachsub-encoder outputting one stream, wherein each sub-encoder is providedwith a property of the stream that is outputted by the sub-encoder, anda layered or multiple-description encoder outputting a plurality ofstreams forming a number of decodable subsets, wherein said encoder isprovided with a property for each decodable subset that is outputted bysaid encoder.
 14. The method according to claim 3, wherein the encoderincludes one or more of the following: a plurality of sub-encoders, eachsub-encoder outputting one stream, wherein each sub-encoder is providedwith a property of the stream that is outputted by the sub-encoder, anda layered or multiple-description encoder outputting a plurality ofstreams forming a number of decodable subsets, wherein said encoder isprovided with a property for each decodable subset that is outputted bysaid encoder.
 15. The method according to claim 5, further comprisingobtaining estimates of transmission quality measures of the decodablesubsets of the streams by modeling the measure of the rate that may beused to transmit signals to the receiver.
 16. The method according toclaim 15, further comprising controlling the encoder to output thedecodable subsets of the streams in accordance with the obtainedestimates of transmission quality measures of the decodable subsets ofthe streams.
 17. The method according to claim 15, wherein the measureof the rate that may be used to transmit signals to the receiver ismodeled using a continuous stochastic variable while minimizing thedistortion perceived by the receiver.
 18. The encoder according to claim7, wherein the control unit is further configured to obtain estimates oftransmission quality measures of the decodable subsets of the streams bymodeling the measure of the rate that may be used to transmit signals tothe receiver.
 19. The encoder according to claim 18, wherein the controlunit is further configured to control the encoder by outputting thedecodable subsets of the streams in accordance with the obtainedestimates of transmission quality measures of the decodable subsets ofthe streams.
 20. The encoder according to claim 18, wherein the controlunit is further configured to model the measure of the rate using acontinuous stochastic variable while minimizing the distortion perceivedby the receiver.